Question

Pfv me ajudem, e importante.

Answer 1

6) Cossecante no segundo quadrante é positiva:

$sen \ x= \frac{1}{6}\\\\ cossec \ x = \frac{1}{sen \ x}\\\\ cossec \ x = \frac{1}{ \frac{1}{6} }\\\\ cossec \ x = 1.\frac{6}{ 1 }\\\\ cossec \ x = 6$

7)

$tg \ y=9\\ tg(x+y)=11\\\\ tg(x+y)=\frac{(tg \ x) + (tg \ y)}{1-(tg \ x).(tg \ y)}\\\\ tg(x+y)=\frac{(tg \ x) + 9}{1-(tg \ x).(9)}\\\\ \frac{(tg \ x) + 9}{1-(tg \ x).(9)}=11\\\\ \frac{(tg \ x) + 9}{1-9.(tg \ x)}=11\\\\ (tg \ x) + 9=11[ 1-9.(tg \ x) ]\\\\ (tg \ x) + 9=11-99.(tg \ x) \\\\ (tg \ x) +99.(tg \ x)=11-9 \\\\ 100.(tg \ x)=2 \\\\ (tg \ x)=\frac{2}{100} \\\\ (tg \ x)=\frac{1}{50}$

8)

$cos \ x=\frac{1}{2}\\\\ sen \ x=\frac{\sqrt{3} }{2}\\\\ sen \ 2x = 2.(sen \ x).(cos \ x)\\\\ sen \ 2x = 2.(\frac{\sqrt{3} }{2}).(\frac{1}{2} )\\\\ sen \ 2x = \frac{\sqrt{3} }{2}$